John Boehner is leading Republican opposition to legislation that would subsidize dairy industry.

WASHINGTON—Negotiators working on the long-delayed farm bill navigated major political land mines on food stamp funding and crop insurance only to hit a last-minute hurdle this week: government support for the dairy industry.

Lawmakers trying to wrap up the legislation had hoped to reach a final framework perhaps as early as this week, but a dispute about part of a proposed dairy program has stalled progress. House Speaker John Boehner (R., Ohio) and a bipartisan group of House lawmakers have been engaging in an...